Development Of Copula-based Approaches For Water Resources Systems Risk Assessment And Management

There exists a variety of uncertainties and complexities in water resources system. However, it is difficult for existing hydrological simulation methods to quantify the uncertainties and nonlinear relationships between hydrological variables. Additionally, the traditional water resources optimization models have great limitations in dealing with multiple uncertainties and nonlinear interactions. Therefore, this article follows an idea of "stochastic hydrological simulation-inexact optimization-risk analysis". A maximum entropy-copula method has been developed for simulation of steamflow in Xiangxi River watershed. Different frequency analysis methods have been merged into the copula framwork to analyze their effects on simulation results. After this, a maximum entropy-copula based Bayesian network method has been proposed for simulation of streamfLow in Kaidu River watershed in order to directly reflect interactions among random variables. The copula function has been introduced into the joint chance-constraint programming for water management and risk analysis to effectively represent and solve stochastic uncertainties and nonlinear interactions in constraints. The limitation that the traditional joint chance-constraint programming can only reflect the linear relationships among random parameters has been overcome. A pplications of copula in water resources system analysis under uncetainty have been expanded. As water management schemes are significantly effected by the subjective factors from decision makers, the fuzzy random value-at-risk based water allocation model has been proposed for risk analysis of water resources system with fuzzy-interval dual uncertainties and stochastic uncertainties to balance the system satisfactions, feasibility degrees and risk levels. Main contents and innovations of this research are as follows:(1) The maximum entropy-copula method is developed for simulation of streamflow in Xiangxi River watershed. The proposed method can generate the probability distributions of monthly streamflows and effectively capture the correlations between the adjacent monthly streamflows. Results indicate that there exist upper tail dependence between adjacent monthly streamflows in Xiangxi River watershed. Comparison between the maximum-entropy-copula and Pearson type Ⅲ based copula methods shows that the maximum entropy method can reflect the statistical characteristics of monthly streamflow without any assumption, getting better performance than Pearson type Ⅲ based copula method on simulation of streamflow in Xiangxi River watershed.(2) The maximum entropy-copula-Bayesian network method has been proposed to simulate monthly streamflow in Kaidu River watershed. The proposed method is a combination of maximum entropy-copula method and Bayesian network, which can directly generate the marignal, joint and conditional distributions of hydrological variables, with the prior information reflected in the process of simulation. Compared with the results generated by maximum entropy-copula method, those generated by maximum entropy-copula-Bayesian network method are more accurate. The corresponding errors have been controled effectively.(3) The copula-based inexact water allocation model has been proposed through combing copula into the two-stage joint probability constraint programming model to reflect the interactions among constraints. The nonlinear dependence among random parameters in the capacity constraints of reservoirs have been reflected and solved while maximizing the economic benefit of the water resources system. Compare with the traditional two-stage joint probability constraint programming, the copula based inexact stochastic programming is more applicable for reflecting nonlinear dependece between random variables in the joint chance constraints.(4) The fuzzy random (conditinal) value-at-risk based inexact water allocation models have been proposed to tackle random variables, dual uncertainties presented as fuzzy boundary interval numbers and the associated risks of water loss. The risk of water loss can be quantified and controlled in fuzzy environment by the fuzzy random value-at-risk and conditional value-at-risk methods. The developed methods can help balance tradeoffs among the satisfactions of system benefits, the risk levels of water loss and the feasibility degrees of constraints. A multi-level factorial design approach has been used to identify interactions between the feasibility degrees and risk levels and to reveal the relationships (including curvilinear relationship) between these factors and the responses. Compared with the fuzzy random value-at-risk based two-stage stochastic programming model, the fuzzy random conditional value-at-risk based model can provide more strict policy of risk aversion, and can relief the unbalanced phenomenon of water resources allocation.